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Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games

Author

Listed:
  • Liron Ravner

    (Department of Statistics, University of Haifa, Haifa 3498838, Israel)

  • Ran I. Snitkovsky

    (Coller School of Management, Tel Aviv University, Tel Aviv 6997801, Israel)

Abstract

We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic updating of the strategy at regeneration times. Under mild assumptions on the utility function and on the regenerative structure of the queueing process, the algorithm converges to a symmetric equilibrium strategy almost surely. This yields a powerful tool that can be used to approximate equilibrium strategies in a broad range of strategic queueing models in which direct analysis is impracticable.

Suggested Citation

  • Liron Ravner & Ran I. Snitkovsky, 2024. "Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games," Operations Research, INFORMS, vol. 72(6), pages 2698-2725, November.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:6:p:2698-2725
    DOI: 10.1287/opre.2021.0306
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